Results 11 to 20 of about 53,501 (261)
Seven Small Simple Groups Not Previously Known to Be Galois Over
Mathematics, 2022 In this note we realize seven small simple groups as Galois groups over Q. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of ...
Luis Dieulefait +2 more
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Divisibility and laws in finite simple groups [PDF]
Mathematische Annalen, 2015 20 pages, no figures; v3 completely rewritten with new co-author and new ...
Gady Kozma, Andreas Thom
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Finite groups with the same conjugacy class sizes as a finite simple group [PDF]
International Journal of Group Theory, 2019 For a finite group $H$, let $cs(H)$ denote the set of non-trivial conjugacy class sizes of $H$ and $OC(H)$ be the set of the order components of $H$. In this paper, we show that if $S$ is a finite simple group with the disconnected prime graph and $
Neda Ahanjideh
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Products of squares in finite simple groups [PDF]
Proceedings of the American Mathematical Society, 2011 The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange’s four squares theorem.
Liebeck, Martin W. +3 more
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Groups with a Strongly Embedded Subgroup Saturated with Finite Simple Non-abelian Groups
Известия Иркутского государственного университета: Серия "Математика", 2020 An important concept in the theory of finite groups is the concept of a strongly embedded subgroup. The fundamental result on the structure of finite groups with a strongly embedded subgroup belongs to M. Suzuki.
A.A. Shlepkin
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Covering Theorem for Finite Nonabelian Simple Groups
مجلة بغداد للعلوم, 2007 In this paper, we show that for the alternating group An, the class C of n- cycle, CC covers An for n when n = 4k + 1 > 5 and odd. This class splits into two classes of An denoted by C and C/, CC= C/C/ was found.
Baghdad Science Journal
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On homogeneous spaces with finite anti-solvable stabilizers
Comptes Rendus. Mathématique, 2022 We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alternating groups for $n\ne 6$ and all 26 sporadic simple groups. We prove that,
Lucchini Arteche, Giancarlo
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On recognizing groups by the bottom layer [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 The article discusses the possibility of recognizing a group by the bottom layer, that is, by the set of its elements of prime orders. The paper gives examples of groups recognizable by the bottom layer, almost recognizable by the bottom layer, and ...
V.I. Senashov, I.A. Paraschuk
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Quantitative characterization of finite simple groups: a complement [PDF]
International Journal of Group TheoryIn this paper, we summarize the research on the characterization of finite simple groups and the study of finite groups based on their ``set of element orders" and ``two orders" (the order of the group and the set of element orders). We also discuss some
Wujie Shi
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Alperin weight conjecture and related developments
Bulletin of Mathematical Sciences, 2022 The Alperin weight conjecture is central to the modern representation theory of finite groups, and it is still open, despite many different approaches from different points of view.
Zhicheng Feng, Jiping Zhang
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